Conformal transformation: Difference between revisions
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It is often profitable to study [[wave equations|nonlinear wave equations]] using '''conformal transformations of spacetime'''. The [[Lorentz transformation]]s, translations, scaling, and time reversal are the most obvious examples, but [[conformal compactification]] (mapping <math>R^{d+1}</math> conformally to a compact subset of <math> S^d x R</math> known as the [[Einstein diamond]]) is also very useful, especially for global well-posedness and scattering theory. One can also blow up spacetime around a singularity in order to analyze the behaviour near that singularity better. | It is often profitable to study [[wave equations|nonlinear wave equations]] using '''conformal transformations of spacetime'''. The [[Lorentz transformation]]s, translations, scaling, and time reversal are the most obvious examples, but [[conformal compactification]] (mapping <math>R^{d+1}</math> conformally to a compact subset of <math> S^d x R</math> known as the [[Einstein diamond]]) is also very useful, especially for global well-posedness and scattering theory. One can also blow up spacetime around a singularity in order to analyze the behaviour near that singularity better. | ||
[[Category: | [[Category:transforms]] | ||
[[Category:geometry]] | [[Category:geometry]] | ||
Latest revision as of 06:56, 31 July 2006
It is often profitable to study nonlinear wave equations using conformal transformations of spacetime. The Lorentz transformations, translations, scaling, and time reversal are the most obvious examples, but conformal compactification (mapping conformally to a compact subset of known as the Einstein diamond) is also very useful, especially for global well-posedness and scattering theory. One can also blow up spacetime around a singularity in order to analyze the behaviour near that singularity better.
